# Radiation reaction of classical hyperbolic oscillator: experimental signatures

## TL;DR

This paper investigates how classical charges radiate and transfer energy during hyperbolic oscillations, highlighting the role of preacceleration and quantum effects, and proposes experimental tests for classical electrodynamics predictions.

## Contribution

It reveals the importance of preacceleration in energy transfer during boundary crossings and critiques the Landau-Lifshitz approximation's accuracy in classical radiation reaction.

## Key findings

- Energy transfer via Schott energy during boundary crossing.
- Preacceleration is essential for correct energy accounting.
- Classical predictions can be experimentally tested through radiation frequency chirping.

## Abstract

When accelerated by a constant force in the lab frame, a classical charge experiences no self force. In this case, the particle radiates without dissipating its kinetic and potential energy. But what happens when the particle enters another region with equal and opposite acceleration? Does the oscillating charge lose its mechanical energy similar to a radiating dipole, even though it seems to lose no mechanical energy within each region of constant acceleration? In this paper, I will show how mechanical energy is transferred to radiation energy via the Schott energy when the particle crosses the boundary between the two regions. In particular, I will show how preacceleration, which is usually regarded as an unphysical effect of the Lorentz-Abraham-Dirac self force, is essential for the energy transfer. Moreover, I will show that the commonly adopted Landau-Lifshitz approximation, which removes preacceleration, introduces second-order secular energy error. On a more fundamental level, the validity of classical electrodynamics is in fact questionable because quantum effects are likely important. The classical prediction can be tested experimentally by observing frequency chirping of radiation, whereby micro physics leaves signatures on macroscopic scales. The required experimental accuracy is estimated. Trap experiment of this type is complementary to collider experiments that endeavor to observe radiation reaction for elementary particles.